The Claimed Priority Patents and Applications disclosed a system, apparatus, and method to produce a uniformly magnified three-dimensional image of a three-dimensional scene in such manner as to preserve the depth to height and width relationship of the image as it existed prior to magnification. This method requires the three-dimensional image prior to magnification to be rendered as an array of two-dimensional images by some form of matrix lens array, such as a fly's eye lens. This array of two-dimensional images is called an integral frame. Were this integral frame to be magnified by some magnification factor, and then viewed or projected through a new matrix lens array that has been scaled up from the lens array that produced the original array of two-dimensional images, such that the scaling factor is equal to the magnification (i.e., the focal length and diameter of each lenslet must be multiplied by the same magnification factor), a new three-dimensional image would be produced that would be magnified by the same magnification factor, and all image dimensions would be magnified by the same factor such that all dimensions of the final three-dimensional image would be proportional to the dimensions of the original image. The utility of magnifying three-dimensional images using this method would be the ability to enlarge holograms or integral photographs or other media from which three-dimensional images are produced, or to project still or moving three-dimensional images before a large audience.
The magnification principle is illustrated in FIG. 1. Object 1 is photographed by matrix lens array 2, thereby producing integral photograph 3. Integral photograph 3 is then magnified to give integral photograph 4 which is then placed behind matrix lens array 5. This combination yields magnified image 6.
It must be noted here, that during scaling-up, the (F/#) of the lenslets remains constant. In this case, the equation for (F/#) is:(F/#)=f/dwhere                f=the focal length of a lenslet; and        d=the diameter of a lenslet.        
Examples of several different traditional matrix lens arrays are disclosed, and in all cases the focal lengths and diameters of the lenslets are scaled-up uniformly by the magnification factor. In one embodiment, an array of cylindrical lenslets is used. This type of array is known as a lenticular sheet or a Bonnet screen. In this case, the lenslet diameter is a meaningless term. Instead, the focal lengths and horizontal widths of the lenslets are scaled-up uniformly.
All of the examples of matrix lens arrays disclosed in the Claimed Priority Patents and Applications are configured such that adjacent lenslets touch each other. If the lenslets do not touch, maintaining the (F/#) constant during the scaling-up process will not work. In this case, the equation for (F/#) is the same as above, where d is known as the aperture.
It would be desirable to have a system and method for uniformly magnifying three-dimensional images where any imaging array could be used. In the general case, imaging elements substitute for lenslets, although imaging elements may comprise lenslets. They could be holographic optical elements or they could even be pinholes. Adjacent imaging elements may or may not touch each other. Such an imaging array should be able to be comprised of different types of elements within the same array. The imaging arrays could have a matrix arrangement of imaging elements, a linear arrangement of imaging elements, or any other arrangement of imaging elements. They should be able to have local arrangements of imaging elements that are different from other local arrangements on the same array. The arrays need not be planar. The original imaging array that captures an image of the three-dimensional scene need not necessarily have the same types of imaging elements as the array that reconstructs the magnified three-dimensional image. The only requirement is that the imaging arrays have a fixed geometric relationship to each other. Similarly, they must also have a fixed geometric relationship to the integral frames upon which they operate. Finally, one should be able to draw or print the elemental images of the integral frame without the requirement of a first imaging array to capture an image of the three-dimensional scene. For example, this technique would be used to produce three-dimensional cartoons.